[Copyright is held by the author/owner(s).
SIGIR’03, July 28-August 1, 2003, Toronto, Canada.
ACM 1-58113-646-3/03/0007]

Abstract reads

"In this paper, we introduce the fractal summarization model based on the
fractal theory. In fractal summarization, the important information is captured
from the source text by exploring the hierarchical structure and salient
features of the document. A condensed version of the document that is
informatively close to the original is produced iteratively using the contractive
transformation in the fractal theory. User evaluation has shown that fractal
summarization outperforms traditional summarization."

I don't have a great deal to say really apart from that JÃ¼rgen Klenk, Gerd Binnig, GÃ¼nter Schmidt, also from IBM looked into this as well concerning networks.

I guess different levels of summarisation are needed for different things, so many methods exist:

TF*RIDF, one of its variants residual IDF - commonly used in IR, where the expected document frequency of a term according to the poisson model ("computes a log linear regression fit of the model specified in the CHARACTER variable Model.")

Mutual Information checks the association between words

Information Gain is a weighting method that measures the relevance of a term to its document.

I didn't only mention vector based methods. Summarisation using semantics is always used. Even in OLAP tasks in relational and multi-dimensional spaces. SD-Form Semantics Model is another example as well. I wanted to bring up alternative methods too. Even I make heavy use of semantics. Fractal methods have been used elsewhere as well, especially in data mining. The cool thing about your paper was the application.

No problem, but let's try to keep all threads to one-topic-at-a time, so others can benefit from reading the posts without having to resort through topics. In this way we all stay on-topic.

Xan, if you feel other topics might add value to users, please feel free to open a new thread for that purpose. We all are trying to keep discussions to one topic per thread, so the SEW forums will not look like a blog.

This fractal Summarization paper is helping out, especially relative to copy writing-- phrase and sentence location within a document. Following the references has also led to other copy-writing tips, such as:

I always thought it was magic how google got its snippets, now I see the broad logic behind it.

Hopefully, this fractal summarization plus on-topic co-occurring words can push our pages up a few positions. Also- at worst case it is a neutral consequence for reader of web page, the "summary tecniques" may even better the web page from the users point of view.

I wondered if you could clear some things up for me. I read your article on the fractal things, and I had some questions, actually we have some questions. I forwarded the article to a few collegues, and the feedback was that more info was needed to understand the claims:

"trying to convince colleage scientists on the fractal nature of everything"
That sounds like an ambitious and perhaps slightly misguided task.
Sure many things can be modeled by fractals to a point. E.g. the texture on
your desk, the coast of Britain, etc. But fractal models don't carry on
past the atomic level (as far as I know anyway, maybe someone has come up
with a way to model the 'fractal' nature of atoms and quarks etc); they are
only useful modeling real life phenomena somewhere in between a high-level
topical abstraction and the atomic level.

"Rather than getting into theoretical details, I prefer to illustrate one of
many experiment one could perform"
This is fine, but where is the experiment documented? I see you have written your ideas on this, but I don't see the experiments. They would be useful for people to be able to see the results and decide if they are convincing or not.

On your first page "the fractal nature of semantics".
The paper you cite: "Fractal summarization: summarization based on fractal theory"(2003) does not in anyway suggest that semantics have a fractal nature. The summarization experiments are purely statistical. Semantics are very unlikely to be fractal. I have submitted to SIGIR and am no stranger to it, and 2003 was a little while ago in terms of research. I mean "semantics" has different meanings, fractal semantics are used in imaging technology, art, things like that.

"Thus, contrary to popular opinion and statements found in the literature on
search engine marketing, a search in EXACT mode not necessarily is a search
for phrases."
I don't think EXACT search queries necessarily are phrases they are just called such by researchers for lack of a better term. So I am not sure what you're saying is against popular opinion.

I think you have a lot of good ideas, but they need to be more than that to convince scientists at least, and the more savvy of your readers. Lots of people have good ideas, even those that don't work are interesting as they show us what doesn't work, which can be equally as important. Experiments need to be properly documented for anything at all, and tested on different environments.

Thus ever suggesting that IR work "only works in the lab" is wrong as we are obliged to test in all environments to write credible experiment documentation.

No dig Orion, just procedures from this side of the wall is all. Would appreciate more info! This isn't unusual.

I'm fully aware of your concerns and questions from you and your colleages. From time to time similar questions arise from both sides (IR and SEO folks). It will be an honor to write a response to these. Just give me some time. We are currently busy addressing some problems in our consulting practice.

By the way, from which university you graduated and in what year? I would also like to know more about yur colleagues. Who are they?

So, in other words, there is no way of confirming any claim in the sense that you have a formal education on IR or that you possibly earned a graduate degree or PhD from a university, nor we are able to confirm who you are or who your research colleagues you referred to are. I’m disappointed because I was thinking in contacting your peers and university administrators for a serious talk and perhaps some collaborative work. Without that information, this may not be possible. Feel free to PM with that information.

I don’t get it. What’s wrong with saying, hey I graduate from this or that university (e.g., Stanford, MIT, Harvard, etc) in the year of… My colleagues John Doe and Jane Doe are working with me on… Fine with me. You are free not to show your true identity and colors. I have no problem when I need to respond to someone questioning my work. Nothing new here.

However, you must be aware that if you make any claim about yourself, your background or reference to your colleagues or any critique to others, you better be ready to be questioned and criticized as well. It is not fair for users of SEWF when then you don’t support your claims or hold back information about yourself or your colleagues. Why then make claims in the first place? Are you that desperate for attention? You see, one cannot go around life questioning or criticizing others and not expect to be questioned and criticized as well. Whatever you do, that’s fine with me. Still I wish one day we can meet at a scientific conference or a SES, honestly.

You also criticize some of my online writings and that’s fine, since are not intended for publications in scientific journals. True that my published work writing style is different from whatever is online. That’s why journals have editorial policies. BTW, Have you published in scientific journals? If so, in which one, when and with whom? Are you a referee for a scientific publication or journal? For which one? I would be happy to know or verify that information. You also claim have talk with AIRWeb folks. I would like to know with whom and when.

You see, very few (Nacho and close friends) know this: Few months ago I was welcome to become referee of JASIS by its online editor. I was also invited to write an article for the publication. I’m also happy to mention that I’m also a book reviewer for academic colleagues and invited to do contribute articles and review books for many other marketing colleagues, some of which are respected members of this forum and others that are not (Prof. David Grossman, Mike Grehan, Ian Mcanerin, Dan Thies, Chris Boggs, sorry if I forget names).

FRACTAL GEOMETRY EVERYWHERE

On the question of fractals, many still don’t get it and still thinking fractal is just for measuring coastlines, image compression or for characterizing textures. Others don’t even get it: Fractal is Nature’s Language. I believe you should be aware that there is plenty of research and documentation on fractals, not only as it relates to the Web, but also in the area of fractal relevancy, latent semantic indexing, fuzzy logic, datamining, semantics, linguistics, psychology, neurology, etc…

With regard to EF-Ratio and what you colleagues think about, again, without knowing who they are, I cannot address their concerns. However, I’ll be please to publish soon some articles on the metric and how it is used by marketers and keyword researchers. Sorry to hear you did not attend SES, NY.

With regard to what is an EXACT search, I may need to mention the name and titles of well known marketers that have been even published books and articles stating this is a search for phrases, which of course is not. Precisely, this is another fallacy debunked.

With regard to your accusation of me trying to apply fractals to everything, I have been conducting research in applied fractal since the late 80’s and presented at international conferences on fractals and chaos back in the early 90’s (before the inception of search engines) and published on the subject. My PhD work is on applied fractal geometry. I have applied this to many dissimilar subjects (chemistry, science education, the web, etc). Sure I may sound biased. Hey, but let see what others have written about the subject.

Back in 1998, Tim Berners-Lee, inventor of the Web, realized what we knew long ago in the fractal and non linear dynamic circles, that the Web has fractal nature. In the link above, he quotes the relevancy of Jon Kleinberg’s work in connection with fractal arguments. He writes

“Clustering algorithms can produce globs of various sizes, and a measure of the chewiness of a web may be that the cluster sizes have a Zipf distribution. For example, using Jon Kleinberg's algorithm (which for a link matrix A associates concepts with the eigenvectors of A*A), the strength of the cluster is the value of the eigenvalue, and (while this does not directly indicate size) an interesting test would be on the relative absolute values (squares?) of successive eigenvalues…..”

“Well, here I was thinking that while it is intuitively clear that society has to be fractal, I didn't know a mathematical justification for it, when Jon Kleinberg comes up with what for me is his second cool web result. This is a paper takes the case of a two-dimensional grid. It imagines each cell having a certain distribution of links of various lengths. It demonstrates that in order to achieve the connectivity a la 6 degrees of separation which scales with the log of the size of the system, then the distribution of link density as a function of distance must be precisely an inverse-square law. That is, each cell must have the same number of links (on average) to cells 1-10 squares away as to cells 10-100 away, etc. Anything more local or more global leads to less of a small-world phenomenon: this is the only scalable solution.”

“Algorithmic tools for searching and mining the Web are becoming increasingly sophisticated and vital. In this context, algorithms that use and exploit structural information about the Web perform better than generic methods in both efficiency and reliability.We present an extensive characterization of the graph structure of the Web, with a view to enabling high-performance applications that make use of this structure. In particular, we show that the Web emerges as the outcome of a number of essentially independent stochastic processes that evolve at various scales. A striking consequence of this scale invariance is that the structure of the Web is "fractal"---cohesive subregions display the same characteristics as the Web at large. An understanding of this underlying fractal nature is therefore applicable to designing data services across multiple domains and scales.We describe potential applications of this line of research to optimized algorithm design for Web-scale data analysis.”

3. JIM OTTAVIANI AND THE FRACTAL NATURE OF RELEVANCE
The fractal nature of relevance: a hypothesis; Journal of the American Society for Information Science (JASIS). May 1994,v.45, no.4., pp.263-272.
Back in 1994, Jim Ottaviani, Head of Reference and Information Services, Media Union Library (5/96 - present) University of Michigan, Ann Arbor, MI published his work “The Fractal Nature of Relevance”. Few months ago I contacted him about a copy of his work, but unfortunately he mentioned is only available through university library exchanges. I’m sure you can make a request through a local university. If you can’t, try JASIS.

There are also several references to Ottaviani’s work through ACM, I think. Here is one, courtesy of Dean M. Riley , Systems Librarian, Moody Library, Houston Baptist University (1996)

"With each different conception of the problem (query) the searcher can identify useful information. Creating one final retrieval set does not solve the problem, but by retrieving bits of information in a series of stages, the process as well as the interim results solve it . . .the berries are scattered on bushes; they do not come in bunches" (Ottaviani, p.264). This journal writer reminds us that documents that answer the question are obviously relevant but so are the documents that help us refine the search and point us in new directions to find what we need (Ottaviani, p.265).” http://fc.hbu.edu/~dmriley/Internet/relevance.htm

5. FRACTAL DIMENSION, LSI and Dimensionality Reduction

In FRACTAL DIMENSION FOR DATA MINING, http://www.cald.cs.cmu.edu/Education...dd_project.pdf Krishna Kumaraswamy from Center for Automated Learning and Discovery, Carnegie Mellon University find applications of fractals to Latent Semantic Indexing and the problem of dimensionality reduction. He writes

“In this project, we introduce the concept of intrinsic fractal dimension of a data set and show how this can be used to aid in several data mining tasks. We are interested in answering questions about the performance of a method and also in comparing between the methods quickly.

In particular, we discuss two specific problems, dimensionality reduction and vector quantization. In each of these problems, we show how the performance of a method is related to the fractal dimension of the data set.”
See also

Erhard Bieberich, Department of Biochemistry and Molecular Biophysics, Medical College of Virginia Campus of Virginia Commonwealth University, writes
“This study aims at a neurochemical approach to the "hard" philosophical mind-body problem: the search for a neuronal correlate of consciousness. The scattered pattern of remote areas in the human brain simultaneously busy with single perceptions has left us with the unanswered questions why, where, and how the neuronal activity gives rise to a unified conscious observation of the outer world in a space inside of the human brain. In this study, conscious perception of temporally and spatially distinct events by an inner observer, the self, is treated as a topological problem demanding for a correlation of the self with a particular orchestration of neuronal or neurochemical activity triggered by action potentials.

According to a novel concept of "topological neurochemistry" it is assumed that three features of the human brain are necessary in order to generate consciousness: 1) A network of neurons with dendritic branching structure and re-entry signaling of action potentials. 2) A macromolecular lattice structure as part of the neuron which is excitable or affected by action potentials. 3) A spatial superposition of action potentials which underlies conscious perception but reveals not necessarily the same topology as the space perceived in consciousness. Several molecular models for the generation of consciousness and the self will be discussed, and a new concept, the "fractal approach", will be introduced. Mathematical theory and experimental methods for investigation of human consciousness will be presented.”

7. ARE WE ABLE TO CHARACTERIZE SEMANTIC WEB BEHAVIOUR?http://dmag.upf.es/livingsw/papers/S...bBehaviour.pdf
Gil, García, and Delgado from Universitat Pompeu Fabra (UPF), Spain research several models (Self-Organized Critically, SOC, Complex Systems, CS Patterns, Barabasi’s Scale-Free Networks (BA Model) and the Semantic Web. They found many fractal and power law behaviors. Very enlightening work.

8. INTRODUCTION TO SOCIAL FUZZIOLOGY

http://www.zulenet.com/VladimirDimit...ocialFuzz.html
In this work, Vladimir Dimitrov University of Western Sydney writes
“Each dynamical process is intersected and interwoven by innumerable simultaneously existing dynamical processes. This infinitive interrelationship of all that exists in the dynamic structure of the universe is reflected on a multitude of scale levels, and thus resemble fractals in chaos theory.

One cannot meaningfully describe events occurring at one level of this structure without taking into consideration the relationship of this level with the levels in which it is embedded and with the levels which are embedded in it. This immediately 'injects' a dose of irremovable fuzziness into the description of each level, which is again reflected in the description of the dynamical structure as a whole.”

“By influencing the ways we think and feel, meanings self-propel their growth - they act as magnets attracting more and more thoughts and feelings, which support them and make them more definite, more categorical, more stable. For example, once the scholars made sense of what Mandelbrot wrote about fractals, they actively started to generate a huge amount of ideas and accumulate information confirming the meaning of fractals in many branches of the human inquiry, so this meaning became clearer, more definite and more stable.”

“The most exceptional and enigmatic property of the human brain is given by its ability to generate a mind inside of itself. By the virtue of being conscious, the human mind experiences a "world" of objects, sensations, and emotions. This world is a product of informational processing and resides completely inside of the brain. Any conscious experience, however, appears to arise from a world projected to the outside of the brain. The mind then merges the perception of the world with an inner quality of emotion and a feeling of being an ontogenetic unity. This inner observer is aware of itself, it is self-concious with an impression of being a perpetual entity with memories and a unique identity, the "self" (Baars, 1997; Cotterill, 1994; Feinberg, 1997; Strawson, 1997).”

In my opinion, this last reference is one of the most fascinating research work I came across on mind behavioral, consciousness and fractals. Please read it.

So, want more applications of fractals? How about a scientific conference that would include SEOs/SEMs and IR colleagues in which these and other topics are welcome?

I’m working on such a project for the benefit of the industry and universities. If you or your colleagues are interested in participating, please just let us know. Just be aware that as with any scientific conference participant, we must ask for you and your colleagues professional credentials.

"I’m working on such a project for the benefit of the industry and universities. If you or your colleagues are interested in participating, please just let us know. Just be aware that as with any scientific conference participant, we must ask for you and your colleagues professional credentials."

I don't think they will want to. Their credentials are very very good, I am quite sure you will be impressed, especially since you keep quoting SIGIR and things like that.

"So, want more applications of fractals? How about a scientific conference that would include SEOs/SEMs and IR colleagues in which these and other topics are welcome?"

There are plenty of conferences to go to already, and its unnecessary:

I never said fractals were not used, I said they are irrelevant to the nature of semantics.

I think you are annoyed. Thanks for all the citations anyway.

"So, in other words, there is no way of confirming any claim in the sense that you have a formal education on IR or that you possibly earned a graduate degree or PhD from a university, nor we are able to confirm who you are or who your research colleagues you referred to are. I’m disappointed because I was thinking in contacting your peers and university administrators for a serious talk and perhaps some collaborative work. Without that information, this may not be possible. Feel free to PM with that information."

I have a good enough c.v I think orion, and my peers have too, some quite dazzling ones. I wouldn't and couldn't work with you I'm afraid. I am involved in plenty of projects and am paid enough

(Also i don't feel I have to justify my educational background or prove anything)

It is not fair for users of SEWF when then you don’t support your claims or hold back information about yourself or your colleagues. Why then make claims in the first place? Are you that desperate for attention? You see, one cannot go around life questioning or criticizing others and not expect to be questioned and criticized as well. Whatever you do, that’s fine with me. Still I wish one day we can meet at a scientific conference or a SES, honestly.

I have supported my claims, academically. You imply that I have to give out my c.v to be taken seriously. I'm not here to gain anything but some insight Orion. As for attention, I mean, I am not the one claiming to have groundbreaking work to share. Also what do you mean "go around life..." You do not know me do you.

I get criticised all the time Orion and if you are a scientist you should be well used to this and well versed in taking it too. Criticism isn't a negative thing at all, but you seem to think so.
You now making this personal and its not necessary. What scientific conferences do you go to? Ah forget it.

Yes I have published Orion, I should think so!! I don't think its possible to even to a postgrad and not have published (in the UK anyway). Again, I don't want to tell you my name or give any personal information, why are you so keen to get it?

You also claim have talk with AIRWeb folks: Yes, it was someone here, I even added their conference to my blog because I'm a nice kind of person and its interesting too.

"You see, very few (Nacho and close friends) know this: Few months ago I was welcome to become referee of JASIS by its online editor. I was also invited to write an article for the publication. I’m also happy to mention that I’m also a book reviewer for academic colleagues and invited to do contribute articles and review books for many other marketing colleagues, some of which are respected members of this forum and others that are not (Prof. David Grossman, Mike Grehan, Ian Mcanerin, Dan Thies, Chris Boggs, sorry if I forget names)."

I am delighted that your work is going so well, but you do not have to prove anything to me. There's no reason to, I don't mind.

I didn't attend SES because its nothing to do with my work is it. It would seem a bit strange if I did I think. I have just been checking out these forums for a few weeks havn't I.

I still am quite sad that you termed your responses "rebuttals", rather than "discussions".

Its very hard to see how the IR world and this one can come together if there can be no discussion.

Finally, there was no need to take it so personally, that wasn't the intention here anyway. I'm happy to not meddle with your threads anymore if that's more appropriate.

All of them are about structure and not language as such. Mapping vector, hierarchical trees, geometric features, etc... there's your fractal bit. They aren't there to actually do anything with the actual words.

http://informatics.indiana.edu/rocha/univgram.html
Its about routings in the brain and how it deals with words. Its actually a really interesting read. It makes a lot of sense as well, but I don't think it really proves semantics are fractal in nature.

Have a look at Patrick Grim, Gary Mar, and Paul St. Denis. The philosophical computer. Exploratory essays in philosophical computer modeling.
Its about computer languages.

A context-free languages are used on computer science, programming languages (as opposed to regular languages).

formal language theory is "a mode of expression more careful and accurate, or more mannered than everyday speech" - "In mathematics, logic and computer science, a formal language is a set of finite-length words (i.e. character strings) drawn from some finite alphabet, and the scientific theory that deals with these entities is known as formal language theory. "

I seem to only find any reading in relation to computer languages, which really isn't the same at all. There's also plenty in DB's and knowledge management, of course, because data mining, information management, groupware , BI software, ... are all knowledge management systems. Those that are build in a hierarchical way also will have patterns geometric in nature as they purposely are built that way.

I just think there are many ways to refer to semantics, and I feel that the fractal idea is best applied to images, ok computer languages of course, and things like that.

Language semantics in a very simple way is the relationships between words. That's it.

Thanks for the info Orion. That's my conclusion anyway, to each his own.